Problem: John Doe has an n × m table. John Doe can paint points in some table cells, not more than one point in one table cell. John Doe wants to use such operations to make each square subtable of size n × n have exactly k points.

John Doe wondered, how many distinct ways to fill the table with points are there, provided that the condition must hold. As this number can be rather large, John Doe asks to find its remainder after dividing by 1000000007 (109 + 7).

You should assume that John always paints a point exactly in the center of some cell. Two ways to fill a table are considered distinct, if there exists a table cell, that has a point in one way and doesn't have it in the other.

Input

A single line contains space-separated integers n, m, k (1 ≤ n ≤ 100; n ≤ m ≤ 1018; 0 ≤ k ≤ n2) — the number of rows of the table, the number of columns of the table and the number of points each square must contain.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier. 

Output

In a single line print a single integer — the remainder from dividing the described number of ways by 1000000007 (109 + 7).

Examples

Input

5 6 1


Output

45

Note

Let's consider the first test case: 

<image> The gray area belongs to both 5 × 5 squares. So, if it has one point, then there shouldn't be points in any other place. If one of the white areas has a point, then the other one also must have a point. Thus, there are about 20 variants, where the point lies in the gray area and 25 variants, where each of the white areas contains a point. Overall there are 45 variants.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.text.DecimalFormat;
import java.util.*;


public class Main {
    private static int MAXN = 100;
    private static int [] [] C,pC;
    private static final int mod = 1000000007;
    private static int N,K;
    private static long M;
    private static int [] [] dp = new int[MAXN+1][MAXN*MAXN+1];

    private static int add(int a,int b) {
        a += b;
        if (a >= mod) a -= mod;
        return a;
    }
    private static int mul(int a,int b) {
        return (int)((a*(long)b)%mod);
    }
    private static int powmod(int a,long p) {
        if (p == 0) return 1;
        int b = 1;
        for (;p > 1;p >>= 1) {
            if (p%2 == 1) b = mul(a,b);
            a = mul(a,a);
        }
        return mul(a,b);
    }

    private static void init(){
        C = new int[MAXN + 1][MAXN + 1];
        pC = new int[MAXN + 1][MAXN + 1];
        for (int n = 0;n <= MAXN;n++){
            C[n][0] = C[n][n] = 1;
            for (int k = 1;k < n;k++)
                C[n][k] = add(C[n-1][k],C[n-1][k-1]);
            for (int k = 0;k <= n;k++)
                pC[n][k] = powmod(C[n][k],M/N);
        }
    }


    public static void main(String[] args) throws Exception{
        IO io = new IO(null,null);
        N = io.getNextInt();
        M = io.getNextLong();
        K = io.getNextInt();
        init();

        int tmp = 0;
        long cnt = 0;
        dp[N][0] = 1;
        for (int col = N-1;col >= 0;col--)
            for (int r = 0;r <= K;r++){
                for (int x = 0;x <= r && x <= N;x++){
                    tmp = pC[N][x];
                    if (col < M%N) tmp = mul(tmp,C[N][x]);
                    tmp = mul(tmp,dp[col+1][r-x]);
                    dp[col][r] = add(dp[col][r],tmp);
                }
             }
        io.println(dp[0][K]);
        io.close();
    }
}

class point{
    private static DecimalFormat df = new DecimalFormat("#.###");
    double x,y;
    public point(double x,double y){
        this.x = x;
        this.y = y;
    }
    point vec(point to) {
        return new point(to.x - x,to.y - y);
    }
    public double length(){
        return Math.sqrt(x*x + y*y);
    }
    @Override
    public String toString(){
        return "(" + df.format(x) + ", " + df.format(y) + ")";
    }
    double dot(point p) {
        return x*p.x + y*p.y;
    }
    double cross(point p) {
        return x*p.y - y*p.x;
    }
}


class IO{
    private BufferedReader br;
    private StringTokenizer st;
    private PrintWriter writer;
    private String inputFile,outputFile;

    public boolean hasMore() throws IOException{
        if(st != null && st.hasMoreTokens()) return true;
        if(br != null && br.ready()) return true;
        return false;
    }
    public String getNext() throws FileNotFoundException, IOException{
        while(st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    public String getNextLine() throws FileNotFoundException, IOException{
        return br.readLine().trim();
    }

    public int getNextInt() throws FileNotFoundException, IOException{
        return Integer.parseInt(getNext());
    }
    public long getNextLong() throws FileNotFoundException, IOException{
        return Long.parseLong(getNext());
    }

    public void print(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f" ,x);
    }
    public void println(double x,int num_digits) throws  IOException{
        writer.printf("%." + num_digits + "f\n" ,x);
    }
    public void print(Object o) throws  IOException{
        writer.print(o.toString());
    }

    public void println(Object o) throws  IOException{
        writer.println(o.toString());
    }
    public IO(String x,String y) throws FileNotFoundException, IOException{
        inputFile = x;
        outputFile = y;
        if(x != null) br = new BufferedReader(new FileReader(inputFile));
        else br = new BufferedReader(new InputStreamReader(System.in));
        if(y != null) writer = new PrintWriter(new BufferedWriter(new FileWriter(outputFile)));
        else writer = new PrintWriter(new OutputStreamWriter(System.out));
    }

    protected void close() throws IOException{
        br.close();
        writer.close();
    }
    public void outputArr(Object [] A) throws IOException{
        int L = A.length;
        for (int i = 0;i < L;i++) {
            if(i > 0) writer.print(" ");
            writer.print(A[i]);
        }
        writer.print("\n");
    }
}